A semidefinite programming approach for solving multiobjective linear programming

Several algorithms are available in the literature for finding the entire set of Pareto-optimal solutions in MultiObjective Linear Programming (MOLP). However, it has not been proposed so far an interior point algorithm that finds all Pareto-optimal solutions of MOLP. We present an explicit construction, based on a transformation of any MOLP into a finite sequence of SemiDefinite Programs (SDP), the solutions of which give the entire set of Pareto-optimal extreme points solutions of MOLP. These SDP problems are solved by interior point methods; thus our approach provides a pseudopolynomial interior point methodology to find the set of Pareto-optimal solutions of MOLP.Junta de AndalucíaFondo Europeo de Desarrollo RegionalMinisterio de Ciencia e Innovació

Multiobjective optimal power flow using a semidefinite programming-based model

In spite of the significant advance achieved in the development of optimal power flow (OPF) programs, most of the solution methods reported in the literature have considerable difficulties in dealing with different-nature objective functions simultaneously. By leveraging recent progress on the semidefinite programming (SDP) relaxations of OPF, in the present article, attention is focused on modeling a new SDP-based multiobjective OPF (MO-OPF) problem. The proposed OPF model incorporates the classical ϵ-constraint approach through a parameterization strategy to handle the multiple objective functions and produce Pareto front. This article emphasizes the extension of the SDP-based model for MO-OPF problems to generate globally nondominated Pareto optimal solutions with uniform distribution. Numerical results on IEEE 30-, 57-, 118-bus, and Indian utility 62-bus test systems with all security and operating constraints show that the proposed convex model can produce the nondominated solutions with no duality gap in polynomial time, generate efficient Pareto set, and outperform the well-known heuristic methods generally used for the solution of MO-OPF. For instance, in comparison with the obtained results of NSGA-II for the 57-bus test system, the best compromise solution obtained by SDP has 1.55% and 7.42% less fuel cost and transmission losses, respectively.©2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.fi=vertaisarvioitu|en=peerReviewed

Inferring AS Relationships: Dead End or Lively Beginning?

Recent techniques for inferring business relationships between ASs have yielded maps that have extremely few invalid BGP paths in the terminology of Gao. However, some relationships inferred by these newer algorithms are incorrect, leading to the deduction of unrealistic AS hierarchies. We investigate this problem and discover what causes it. Having obtained such insight, we generalize the problem of AS relationship inference as a multiobjective optimization problem with node-degree-based corrections to the original objective function of minimizing the number of invalid paths. We solve the generalized version of the problem using the semidefinite programming relaxation of the MAX2SAT problem. Keeping the number of invalid paths small, we obtain a more veracious solution than that yielded by recent heuristics

Multiobjective Robust Control with HIFOO 2.0

Multiobjective control design is known to be a difficult problem both in theory and practice. Our approach is to search for locally optimal solutions of a nonsmooth optimization problem that is built to incorporate minimization objectives and constraints for multiple plants. We report on the success of this approach using our public-domain Matlab toolbox HIFOO 2.0, comparing our results with benchmarks in the literature